Multidomain State Research Articles

Quantitative analysis of the magnetic domain structure in polycrystalline La0.7Sr0.3MnO3thin films by magnetic force microscopy

The nanoscale magnetic domain structure of the polycrystalline La(0.7)Sr(0.3)MnO(3) granular thin films was imaged with a developed magnetic force microscopy technique by simultaneously detecting both the perpendicular and in-plane components of magnetic field gradients during the same scan of the tip oscillation. The characteristics of both the perpendicular and in-plane magnetic field gradient at the grain edges or the nonmagnetic grain boundary phase for LSMO films were demonstrated and can be used to evaluate the magnetic domain structure and magnetic isolation between neighboring grains. A two dimensional signal transformation algorithm to reconstruct the in-plane magnetization distribution of the polycrystalline LSMO thin films from the measured raw MFM images with the aid of the deconvolution technique was presented. The comparison between the experimental and simulated MFM images indicates that the magnetic grains or clusters are in the single domain (SD) or multi-domain (MD) state with the magnetic moments parallel or anti-parallel to the effective magnetic field of each grain, possibly due to the need for minimizing the total energy. The quantitative interpretation of the magnetic domain structure indicates that the large magnetoresistance in the studied LSMO films is mainly due to tunnel effect and scattering of conducted electrons at the nonmagnetic grain boundary phase related to the different configurations of magnetic domain states between neighboring grains.

Fabrication of a Multidomain and Ultrafast‐Switching Liquid Crystal Alignment Layer Using Contact Printing with a Poly(dimethylsiloxane) Stamp

A compartmentalized multidomain alignment state of a layer of liquid crystal display is achieved using an ultrathin, highly transparent, and ultrafast-responsive alignment layer fabricated by a simple method. The ultrathin alignment layer consists of a self-assembled oligomer layer of poly(dimethylsiloxane) (PDMS) formed by utilizing the oligomers that diffuse out from a PDMS elastomer stamp during a contact printing process.

Intergranular Exchange Coupling Field Under Multidomain State for Stacked Perpendicular Recording Media Evaluated by Ferromagnetic Resonance

The intergranular exchange (coupling) field <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex</sub> of single/stacked granular perpendicular magnetic recording media with a switching field (SF) distribution was measured by ferromagnetic resonance (FMR) by sweeping the external field <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">DC</sub> through the internal effective field <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> . <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> consists of components corresponding to the anisotropy field <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> , the dipole interaction field, the self-demagnetization field, and the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex</sub> for up and down magnetic moments of magnetic grains classified by their SF. FMR measurements were performed for one kind of weak intergranular exchange coupled medium (medium I) and two kinds of strong intergranular exchange coupled media (medium II (single magnetic layer structure) and III (stacked structure)). These measurements revealed that the increase in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex</sub> with decreasing 4π <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> for media II and III was larger than that for medium I. In addition, <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">ex</sub> / <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> was determined to be 0.25 (for grains with low SF) and 0.37 (for grains with high SF) for medium II and 0.34 (for both low and high SF) for medium III under <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">M</i> =0.3. The variation in <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">eff</sub> for the multidomain state was smaller for the strong intergranular exchange coupled media than for the weak intergranular exchange coupled medium. The values normalized by <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">H</i> <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">k</sub> were approximately ± 0.038-0.060, ± 0.008-0.015, ± 0.012-0.030 for media I, II, and III, respectively.

Bit Patterned Structure Fabricated by Kr$^{+}$ Ion Irradiation onto MnBiCu Films

Mn54Bi24Cu21 (15 nm) films with a perpendicular anisotropy were prepared by annealing the sputtered MnCu/Bi multilayer at a temperature of 350 °C. The MnBiCu film had a rather flat surface of Ra = 1.1 nm, and uniform maze domain was observed before the ion irradiation. The magnetization and coercivity of the MnBiCu film were confirmed to disappear after a low Kr+ ion dose of 5 ×1013 ions/cm2. Bit patterned media (BPM) using the MnBiCu (15 nm) films were fabricated by 30 kV Kr+ ion irradiation through electron beam lithography-made resist masks. The surface of the ion-irradiation BPM was almost identical to that of the as-annealed film. The magnetization processes of the bit patterned media were investigated by magnetic force microscope observations after application of the magnetic field. The patterned MnBiCu bits with a size ranging from 500 × 500 nm to 300 × 300 nm have a multidomain state and their magnetization reversals undergo nucleations of the reversed domain and wall propagation. By decreasing the bit size of the patterned MnBiCu, the average switching field Hsf of the bits was increased. This means that the exchange coupling between the patterned bits and the bit edge damage were negligibly small, and shows the possibility of high density ion irradiated planar bit patterned media.

Domain controlled magnetic and electric properties of variable sized magnetite nano-hollow spheres

Here, we report the synthesis of variable sized magnetite (Fe3O4) nano-hollow spheres in one step template free solvothermal method and their size dependent magnetic and electrical properties. Size of the hollow spheres is varied from 100 nm to 725 nm by changing the concentration of capping agent. Trace of Verway transition is found for all sets of spheres and the Verway transition temperature (TV) increases with increasing size of the spheres. The domain structure of these spheres changes from pseudo single domain to multi domain state as the size increases from 100 nm to 725 nm as evident from Day plots. This change in domain structure also changes the magnetic and electric properties of these spheres. Temperature dependent of high field magnetization of the hollow spheres can be well explained by Bloch's power law with higher than the bulk value of Bloch constant. The Bloch exponent varies from 1.94 to 1.69 with increasing size of the spheres. Frequency dependence of electrical conductivity (σ) shows Jonscher's power law type behaviour and bigger spheres are found to be more conductive than smaller ones due to their multidomain configuration.

Piezoresponse force microscopic study of ferroelectric (1 − x)Pb(Sc1/2Nb1/2)O3 − xPbTiO3 and Pb(Sc1/2Nb1/2)O3 single crystals

The microscopic piezoelectric response and ferroelectric domain switching in the (001)-oriented rhombohedral piezo-/ferroelectric (1 − x)Pb(Sc1/2Nb1/2)O3 − xPbTiO3 (PSN-PT) and relaxor Pb(Sc1/2Nb1/2)O3 (PSN) single crystals were studied by piezoresponse force microscopy. PSN-PT shows clear domain structures while the domain contrast of PSN is very weak. For PSN-PT, after being fully poled vertically, its lateral domain structure is still composed of a multi-domain state. Both PSN-PT and PSN crystals respond to positive and negative DC field drives through piezoelectricity. However, their poling behaviors are different. For PSN-PT, during successive applications of a positive external electric field, the areas with piezoresponse in phase with the electric field grow at the expense of domains of opposite piezoresponse, implying a domain switching process via sideway motion of domain walls. On the other hand, in the PSN single crystal, the piezoresponse contrast of the alternatively poled area shows a uniformly fading and enhancing pattern, depending on the direction of the polarization component of the domains relative to the external field. While the domain pattern of PSN-PT and its evolution under an external field behave like a normal ferroelectric material, the domain structure and domain evolution process of PSN appear to be abnormal for a ferroelectric, but consistent with the character of a relaxor.

Micromagnetic states in Fe (001) rectangular epitaxial microstructures: The effect of magnetic anisotropy and aspect ratio

The magnetic structures of Fe (001) epitaxial rectangular elements 100nm thick, 0.25–4μm wide aspect ratio AR 1:4 and 1:8 oriented along the easy (EAM) and hard (HAM) magnetization axes were studied by magnetic force microscopy and micromagnetic calculations. All the elements of 1μm width and wider are in multi-domain states, which type depends on the AR and orientation with respect to EAM. In the elements oriented parallel to EAM at low AR, a diamond state realizes while at larger AR the fundamental state is of Landau type. In the elements with the orientation parallel to HAM at low AR, a cross-tie state is observed and at larger AR the states are of a concertina or a meander type. As the element sizes decrease, the domain wall width does not virtually undergo any changes and the transition from a multi-domain to a quasi-vortex state proceeds through monotonic increase of the sample volume fraction with a non-collinear magnetization distribution. The quasi-vortex state occurs at the width lower than 0.6μm and depends neither on AR nor on the orientation with respect to EAM. The transition from a quasi-vortex to a quasi-single domain state depends on AR and orientation relatively to EAM.

Single domain behaviour of bulk RbMnF3

The temperature dependence of the order parameter of antiferromagnetic RbMnF3 has been measured using neutron scattering. After necessary corrections, single crystal data agree perfectly with data obtained on powder material. Surprisingly, the order parameter of cubic RbMnF3 exhibits the same universal T5/2 temperature dependence as the order parameter of tetragonal MnF2. T5/2 universality class has been identified as characteristic for magnets with one-dimensional continuous dynamic symmetry. It is discussed in some generality that the domain structure is decisive for the dynamic symmetry class. If powder grains are single domain particles one-dimensional behaviour can be anticipated generally. However, bulk single crystals of cubic RbMnF3 should be in the multi-domain state and should exhibit the T2 universality class of isotropic magnets with half-integer spin. Isotropy results by a dynamic averaging process over all differently oriented magnetic domains. Since the magneto-elastic coupling of RbMnF3 is extremely weak it can be assumed that the domain structure is rather coarse. If the domain size is larger than the dynamic length scale of the order parameter the usual averaging process over all domain orientations does not work. Consequently, the observed one-dimensional continuous dynamic symmetry of bulk RbMnF3 is that of an isolated domain.

Giant anhysteretic response of ferroelectric solid solutions with morphotropic boundaries: the role of polar anisotropy

Computer modeling and simulation for the Pb(Zr1-xTix)O3 (PZT) system reveal the role of polar anisotropy on the giant anhysteretic response and structural properties of morphotropic phase boundary (MPB) ferroelectrics. It is shown that a drastic reduction of the composition-dependent polar anisotropy near the MPB flattens energy surfaces and thus facilitates reversible polarization rotation. It is further shown that the polar anisotropy favors formation of polar domains, promotes phase decomposition and results in a two-phase multidomain state, which response to applied electric field is anhysteretic when the polar domain reorientation is only caused by polarization rotation other than polar domain wall movement. This is the case for the decomposing ferroelectrics under a poling electric field with the formation of a two-phase multidomain microstructure, wherein most domain walls are pinned at the two-phase boundaries. Indication of the microstructure dependence of the anhysteretic strain response opens new avenues to improve the piezoelectric properties of these materials through the microstructure engineering.

Single domain vs. polydomain [111] 0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3 single crystal. Polarization switching, dielectric and pyroelectric properties

We introduce a poling treatment to induce a single domain structure in [111] single crystals of 0.72Pb(Mg1/3Nb2/3)O3-0.28PbTiO3 (PMN-PT). The properties obtained differ from those known for domain-engineered [111] PMN-PT single crystals. The dielectric, ferroelectric, and pyroelectric properties of this single domain structure are assessed in comparison to polydomain single crystals that were poled by conventional poling treatment. The attributes of the single domain state are a single switching event that reflects in a discontinuity of polarization at the coercive field, a substantially lower dielectric loss (than the multidomain state), and a higher detectivity for pyroelectric applications.

Low-field microwave absorption in epitaxial La0.7Sr0.3MnO3films that results from the angle-tuned ferromagnetic resonance in the multidomain state

We studied magnetic-field-induced microwave absorption in 100--200 nm thick La${}_{0.7}$Sr${}_{0.3}$MnO${}_{3}$ films on SrTiO${}_{3}$ substrate and found a low-field absorption with a very peculiar angular dependence: it appears only in the oblique field and is absent both in the parallel and in the perpendicular orientations. We demonstrate that this low-field absorption results from the ferromagnetic resonance in the multidomain state (domain-mode resonance). Its unusual angular dependence arises from the interplay between the parallel component of the magnetic field that drives the film into multidomain state and the perpendicular field component that controls the domain width through its effect on domain-wall energy. The low-field microwave absorption in the multidomain state can be a tool to probe domain structure in magnetic films with in-plane magnetization.

Magnetization reversal analysis of a thin B2-type ordered Co50Fe50 film by magnetooptic Kerr effect

The magnetic structure of a thin B2 ordered Co50Fe50 film is determined by vectorial magnetometry using magnetooptic Kerr effect including different polarizations of the incident light and varied directions of the external magnetic field. Both the magnetic reversal process and the magnetic remanence reveal two in-plane magnetic easy axes of different strengths which are not orthogonal. Atypical magnetization curves including multidomain states in magnetic remanence with some magnetic moments providing antiparallel alignment to the direction of the previously applied external field (if projected to the direction of the external field) confirm the appearance of different strong magnetic easy axes. This magnetic structure can be explained by a cubic magnetic anisotropy (CMA) induced by the crystalline film structure superimposed by an additional uniaxial magnetic anisotropy (UMA) which is not parallel to one of the magnetic easy axes of the CMA. The results are compared with the regular magnetic behaviour of a thin A2 ordered Co50Fe50 film with UMA parallel to one of the magnetic easy axes of the CMA.

Effects of heat treatment conditions on the structural and magnetic properties of MgCuZn nano ferrite

Mg0.5Cu0.05Zn0.45Fe2O4 nanoparticles were prepared through sol–gel method using polyvinyl alcohol as a chelating agent. The as prepared sample was annealed at three different temperatures (500°C, 700°C and 900°C). The phase formation, morphology and magnetic properties with respect to annealing temperature were studied using the characterisation techniques like X-ray diffraction (XRD) as well as Fourier transform infrared spectroscopy (FTIR), field emission scanning electron microscopy (FESEM) and vibrating sample magnetometer (VSM), respectively. The crystallite size and magnetisation showed increasing trend with annealing temperature. The coercivity increased up to a particular annealing temperature and decreased thereafter, indicating transition from single domain to multi domain state with increasing annealing temperature. Further, to know the suitability of the material, as a ferrite core, in multilayer chip inductors, the powder sample annealed at 500°C was compacted in the form of torroids and sintered at three different temperatures (800°C, 900°C and 950°C). The permeability showed increasing trend with the increase of sintering temperature since the permeability depends on microstructure. The frequency dispersion of permeability, for the sintered samples, demonstrated high frequency stability as well as high operating frequency. The cut-off frequency for the sintered samples 800°C, 900°C and 950°C is 32MHz, 30.8MHz and 30.4MHz, respectively.

Thickness driven stabilization of saw-tooth–like domains upon phase transitions in ferroelectric thin films with depletion charges

Ionized impurities have nearly always been neglected in discussing the limit of functionality of ferroelectric thin films. One would certainly expect that the thickness limit for functionality would be altered in the presence of ionized impurities, but how this would occur remains unclear. In this article, we analyze the domain structures as well as the phase transition temperatures in films with depletion charges for various film thicknesses. Depletion charges induce a position-dependent built-in field that leads to an inhomogeneous distribution of ferroelectric polarization. Such an inhomogeneity in the polarization results in strong depolarizing fields in films. We show that formation of saw-tooth–type domains is a way to circumvent the depolarizing fields, even in films with ideal electrodes. There is a critical film thickness above which the saw-tooth domains develop. On the other hand, the phase transition of the ultrathin structures with electrodes having a finite screening length, namely real electrodes, is always into the multidomain state during cooling from the paraelectric state, regardless of the presence of depletion charges. An important finding we have is that the transition temperature in films with real electrodes does not depend nearly at all on the depletion charge density unless it is very high (&amp;gt;1026 ionized impurities/m3). Relatively thick films (&amp;gt;8 nm in this work) with real electrodes that have very high depletion charge densities have transition temperatures very similar to those with the same charge density, but with ideal electrodes, making us conclude that thick films with high depletion charge densities will hardly feel the finite screening effects. The results are provided for (001) BaTiO3 films grown on (001) SrTiO3 substrates with pseudomorphic top and bottom metallic electrodes.

Observation and implications of magnetic domains in lateral spin valves

Co/Cu/Co lateral spin valves (LSV), with Co being the topmost layer, are in situ prepared and measured under ultrahigh vacuum conditions. The clean process yields a non-local spin signal of 0.9 mΩ. Scanning electron microscopy with polarization analysis (SEMPA) reveals domain structures in both magnetic electrodes that depend on the LSV dimensions. The spin signal correlates to SEMPA images as well as the anisotropic magnetoresistance of both Co magnets, revealing a strong impact of multi-domain states on the spin signal.

Emergence of a novel optically isotropic transient state with low frequency in a blue phase liquid crystal mixture

The electro-optical hysteresis characteristics in a blue phase liquid crystal system showing multi-domain platelet type body-centred cubic (BP-I) structure at different levels of applied electric field have been investigated. The BP-I state possesses a large degree of hysteresis due to its compact body-centred cubic structure. The hysteresis behaviour is discussed in the context of simulation and theoretical studies reported earlier. When the cell is driven with a low frequency square wave, a novel optically isotropic state with high value of the Kerr constant has been observed. Hysteresis and response time both show relatively lower values in this state with respect to the multi-domain BP-I state.

Observations of laser induced magnetization dynamics in Co/Pd multilayers with coherent x-ray scattering

We report on time-resolved coherent x-ray scattering experiments of laser induced magnetization dynamics in Co/Pd multilayers with a high repetition rate optical pump x-ray probe setup. Starting from a multi-domain ground state, the magnetization is uniformly reduced after excitation by an intense 50 fs laser pulse. Using the normalized time correlation, we study the magnetization recovery on a picosecond timescale. The dynamic scattering intensity is separated into an elastic portion at length scales above 65 nm, which retains memory of the initial domain magnetization, and a fluctuating portion at smaller length scales corresponding to domain boundary motion during recovery.

Phase transitions in ferroelectric-paraelectric superlattices

Within the phenomenological Landau–Ginzburg–Devonshire theory, we discuss the paraelectric-ferrolectric transition in superstructures consisting of ferroelectric and paraelectric layers of equal thickness. The polar axis of the ferroelectric is perpendicular to the layer plane as expected in fully strained BaTiO3/SrTiO3 superstructures on SrTiO3 substrates with pseudomorphic electrodes. We concentrate on the electrostatic effects and do not take into account the boundary conditions other than the electrostatic ones. We find that when the ferroelectric phase transition in the superstructures is into a multidomain state, both its temperature and its character, i. e., the profile of the polarization appearing at the phase transition is strongly influenced by the nature of the near-electrode region. This is also the case for the layer thickness separating the single-and multidomain regimes of the transition. Such a finding makes us question the idea that these superstructures can be thought of as infinite systems, i.e., periodic superstructures similar to a crystal. The irrelevance of this idea in certain conditions is demonstrated by comparing the phase transitions in two different superstructures consisting of ferroelectric and paraelectric layers of the same thickness. In one of them, the ferroelectric layer is in immediate contact with an ideal metallic electrode, whereas at the other boundary, it is the paraelectric layer that is in contact with the electrode. In another superstructure, one paraelectric layer is split in two equal parts which are placed as the first and last layer between the electrodes and the ferroelectric layers which are closest to the electrodes. We show (with some formal reservations) that the phase transition temperature in the first superstructure can be over 100 °C more than in the second one if the material parameters of BaTiO3/SrTiO3 are used for the estimations. Moreover, the profile of the polarization arising at the phase transition is inhomogeneous along the superstructure and has the maximum amplitude in the ferroelectric layer contacting the electrode. We argue that this situation is general and results in smearing of the phase transition anomalies for the layer thicknesses corresponding to multidomain transitions. The work is mainly analyical but numerical methods have been used to support some statements that have been put forward as hypotheses.

Effect of pinning-field distribution on the process of magnetization reversal in Ga1−xMnxAs films

The process of magnetization reversal in a Ga${}_{1\ensuremath{-}x}$Mn${}_{x}$As film is investigated by using angle-dependent measurements of the planar Hall effect. When a small field (e.g., below 25 Oe) is used, the planar Hall resistance (PHR) displays four stable values arising from the formation of four different multidomain states during the rotation of the external field direction over 360\ifmmode^\circ\else\textdegree\fi{}. Two of these correspond to the sample being fully magnetized along one of the easy axes. It is shown that there are two intermediate states which form when a fraction of the domains populates one easy direction (say, [100]), and the remaining fraction populates an orthogonal easy axis (with magnetizations, say, along the [010] direction). It is further shown that the relative populations of the magnetic domains corresponding to the two orthogonal easy axes can be controlled by the value of the applied field during the process of magnetization reversal. This phenomenon can be understood by considering the differences in domain-pinning fields and their distributions required for crossing the [110] and the $[1\overline{1}0]$ directions in the (001) plane of the Ga${}_{1\ensuremath{-}x}$Mn${}_{x}$As film.

Local tunneling magnetoresistance probed by low-temperature scanning laser microscopy

Tunneling magnetoresistance in a vertical manganite junction was investigated by low-temperature scanning laser microscopy (LTSLM) allowing to determine the local relative magnetization M orientation of the two electrodes as a function of magnitude and orientation of the external magnetic field H. Sweeping the field amplitude at fixed orientation revealed magnetic domain nucleation and propagation in the junction electrodes. For the high-resistance state, an almost single-domain antiparallel magnetization configuration was achieved, while in the low-resistance state the junction remained in a multidomain state. Calculated resistance Rcalc(H) based on the local M configuration obtained by LTSLM is in quantitative agreement with R(H) measured by magnetotransport.